We recast the problem of hydrogel swelling under physical constraints as an energy optimization problem. We apply this approach to compute equilibrium shapes of hydrogel spheres confined within a jammed matrix of rigid beads and interpret the results to determine how confinement modifies the mechanics of swollen hydrogels. In contrast to the unconfined case, we find a spatial separation of strains within the bulk of the hydrogel as the strain becomes localized to an outer region. We also explore the contact mechanics of the gel, finding a transition from Hertzian behavior to non-Hertzian behavior as a function of swelling. Our model, implemented in the Morpho shape optimization environment and validated against an experimentally demonstrated prototypical scenario, can be applied in any dimension, readily adapted to diverse swelling scenarios and extended to use other energies in conjunction.
Microscopic high aspect ratio particles have many applications including enhanced delivery of active ingredients and food stability. Here, we develop a simple, scalable process that produces particles with a continuously controllable aspect ratio. Oil-in-water emulsion droplets are quenched and crystallize in the presence of surfactants that facilitate the ejection of the solid oil phase from its liquid precursor. Tuning the ejection and crystallization rates to be comparable, by adjusting the surfactant concentration and quench depth, promotes anisotropic particle growth by continuously ejecting solidified oil from the precursor droplet as the crystallization proceeds. We predict the accessible morphologies using an analytical geometric model that indicates a nonconstant contact angle during the crystallization process. We see that the crystal aspect ratio is dependent on the surfactant concentration, which can be explained as a variation of the maximum growth angle achieved during crystallization.
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or a higher fill fraction when the smaller particles are accommodated in the interstices of the larger spheres. Variation in the packing fraction is explained by a percolation transition, as chains of defects or scars previously discovered in the monodispersed case grow and eventually disconnect the neighbor graph.
